Affordable Access

Publisher Website

On existence of directly finite, only one sided self-injective regular rings

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
144
Issue
1
Identifiers
DOI: 10.1016/0021-8693(91)90131-q

Abstract

Abstract This paper is concerned with the following open problem. Is every directly finite, regular right self-injective ring necessarily left self-injective [2, Open problem 14]? This problem is 21 years old and came from J.-E. Roos [8]. We solve in the negative by giving an example. In the example, we construct a simple regular subring of the rank metric completion of a direct limit of a sequence of matrix rings over a field. Moreover the maximal right quotient ring of this simple regular ring is directly finite and not left self-injective. This result was announced in [6] without proof.

There are no comments yet on this publication. Be the first to share your thoughts.